Entanglement and separability of quantum harmonic oscillator systems at finite temperature

  • Authors:

  • Janet Anders;Andreas Winter

  • Affiliations:

  • Quantum Information Technology Lab, National University of Singapore, Singapore;Department of Mathematics, University of Bristol, Bristol, United Kingdom and Quantum Information Technology Lab, National University of Singapore, Singapore

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2008

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Abstract

In the present paper we study the entanglement properties of thermal (a.k.a. Gibbs) states of quantum harmonic oscillator systems as functions of the Hamiltonian and the temperature. We prove the physical intuition that at sufficiently high temperatures the thermal state becomes fully separable and we deduce bounds on the critical temperature at which this happens. We show that the bound becomes tight for a wide class of Hamiltonians with sufficient translation symmetry. We find, that at the crossover the thermal energy is of the order of the energy of the strongest normal mode of the system and quantify the degree of entanglement below the critical temperature. Finally, we discuss the example of a ring topology in detail and compare our results with previous work in an entanglement-phase diagram.